An increasingly wide range of transmission technologies are available for use in modern electronic communication systems. Contemporary options include multicarrier, spread spectrum, narrowband, and infrared technologies. Although each technology has its own advantages and disadvantages, one particular type of multicarrier transmission—orthogonal frequency division multiplexing (“OFDM”)—has proven to be an exceptionally robust technique for efficiently transmitting data in many applications. OFDM uses a plurality of subcarrier frequencies (“subcarriers”) to transmit data within a channel bandwidth. In contrast to less sophisticated frequency division multiplexing (“FDM”) techniques, which can waste portions of the bandwidth for separation and isolation of subcarrier frequency spectra and avoidance of inter-carrier interference (“ICI”), OFDM increases bandwidth efficiency by significantly overlapping the frequency spectra of its subcarriers within the channel bandwidth. OFDM allows resolution and recovery of the baseband information that has been modulated onto each subcarrier even though the frequency spectra are overlapped. Furthermore, in addition to the more efficient spectrum usage, OFDM provides several other advantages, including a tolerance to multi-path delay spread and frequency selective fading, good interference properties, and relatively simplified frequency-domain processing of the received signals.
For processing, an OFDM receiver typically converts a received signal from the time-domain into frequency-domain representations of the signal. Generally, conventional OFDM receivers accomplish this by sampling the time-domain signal and then applying Fast Fourier Transforms (“FFTs”) to blocks of the samples. The resulting frequency-domain data typically includes a complex value (e.g., magnitude component and phase component, or real component and imaginary component) for each respective subcarrier. Then, the receiver typically applies an equalizer to the frequency-domain representations of the received signal before recovering the baseband data that has been modulated onto each subcarrier. The equalizer can correct for multi-path distortion effects of the channel through which the OFDM signal was transmitted. Some receivers may also use the equalizer to correct for other problems encountered with OFDM communications, such as, for example, carrier frequency offset (i.e., a difference between the transmitter and receiver frequencies), and/or sampling frequency offset (i.e., a difference between the transmitter and receiver sampling clock frequencies). Carrier frequency offset and sampling frequency offset can result in a loss of orthogonality between the subcarriers, which results in inter-carrier interference (“ICI”) and a severe increase in the bit error rate (“BER”) of the data recovered by the receiver.
FIG. 1 (Prior Art) is a block diagram of a conventional multiplier 10 for an OFDM equalizer tap. A typical OFDM equalizer has one or more filters (or “taps”) which receive a tap setting corresponding to a complex correction (e.g., a real correction and an imaginary correction, or a magnitude correction and a phase correction) for each subcarrier (or “subchannel”). The equalizer outputs are typically real (“I”) and imaginary (“Q”) signal components for each subcarrier. Historically, separate I and Q outputs have been provided by an architecture that requires at least four multipliers to multiply the respective complex data input (a+jb) by the respective complex tap setting (c+jd). But, implementing even a single multiplier in digital integrated circuitry requires a large number of logic gates. Consequently, the high number of multipliers that has historically been required to fashion an equalizer has undesirably added to the size and cost of OFDM receiver circuitry. The present invention is directed to overcoming this problem.